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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Structural instability of $ {\rm exp}(z)$


Author: Robert L. Devaney
Journal: Proc. Amer. Math. Soc. 94 (1985), 545-548
MSC: Primary 58F12; Secondary 30D05, 58F10
MathSciNet review: 787910
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Abstract: The entire function $ \operatorname{exp}\left( z \right)$ has a Julia set equal to the whole plane. We show that there are complex $ \lambda $'s near 1 such that $ \lambda {e^z}$ has an attracting periodic orbit. Hence $ {e^z}$ is not structurally stable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787910-2
PII: S 0002-9939(1985)0787910-2
Keywords: Exponential map, Julia set, structural stability
Article copyright: © Copyright 1985 American Mathematical Society